Answer 1:
It depends on what one is trying to test. For example, solving an algebraic equation tests whether one understands the formalism of the basic mathematics, but a thought problem that requires one to develop an algebraic equation that applies to a situation is quite different. There is also substantial debate about underlying cultural factors when writing tests meaning it is difficult in some cases to write a test that is not reliant on ones upbringing. There are no easy answers here unfortunately.
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